A Study on FEA of Torsional Vibration in Geared Shafts

Abstract

Finite element analysis is a sophisticated technology based on the principle of discretization and numerical approximation to solve scientific and engineering problems. In this methodology any structure under consideration is discretized into small geometric shapes and the material properties are analyzed over these small elements. The purpose of this project is to study the simple approach of analyzing the torsional vibration in a branched geared system. The global mass matrix and stiffness matrix of the geared system are obtained using the finite element method (FEM) by aggregating the property matrices of the elements discretized in the shafts present in the torsional system. The masses are lumped in the form of rotors in the geared system. Then equations of motion of the whole vibrating system are defined. A finite assemblage of discrete continuous elements leads to the formulation of the associated eigenvalue equation in the configuration of matrices provides the natural frequencies and the mode shapes of the system. Holzer’s method is also discussed to find the natural frequencies of branched geared systems. And thence the results obtained using Finite Element Method are compared with those obtained by the numerical method as devised by ‘Holzer’.